3D zernike descriptors for content based shape retrieval

Content based 3D shape retrieval for broad domains like the World Wide Web has recently gained considerable attention in Computer Graphics community. One of the main challenges in this context is the mapping of 3D objects into compact canonical representations referred to as descriptors, which serve as search keys during the retrieval process. The descriptors should have certain desirable properties like invariance under scaling, rotation and translation. Very importantly, they should possess descriptive power providing a basis for similarity measure between three-dimensional objects which is close to the human notion of resemblance.In this paper we advocate the usage of so-called 3D Zernike invariants as descriptors for content based 3D shape retrieval. The basis polynomials of this representation facilitate computation of invariants under the above transformations. Some theoretical results have already been summarized in the past from the aspect of pattern recognition and shape analysis. We provide practical analysis of these invariants along with algorithms and computational details. Furthermore, we give a detailed discussion on influence of the algorithm parameters like type and resolution of the conversion into a volumetric function, number of utilized coefficients, etc. As is revealed by our study, the 3D Zernike descriptors are natural extensions of spherical harmonics based descriptors, which are reported to be among the most successful representations at present. We conduct a comparison of 3D Zernike descriptors against these regarding computational aspects and shape retrieval performance.